-3n(5n-9n)=9+8n

Solution for -3n(5n-9n)=9+8n equation:

-3n(5n-9n)=9+8n

We move all terms to the left:

-3n(5n-9n)-(9+8n)=0

We add all the numbers together, and all the variables

-3n(-4n)-(8n+9)=0

We multiply parentheses

12n^2-(8n+9)=0

We get rid of parentheses

12n^2-8n-9=0

a = 12; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·12·(-9)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{31}}{2*12}=\frac{8-4\sqrt{31}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{31}}{2*12}=\frac{8+4\sqrt{31}}{24}
$